One often has to submit a document (e.g., a paper or a dissertation) under some sort of constraint about its size. Sensible people set a constraint in terms of numbers of pages, but there are some that persist in limiting the numbers of words you type.
A simple solution to the requirement can be achieved following a simple observation: the powers that be are unlikely to count all the words of a document submitted to them. Therefore, a statistical method can be employed: find how many words there are on a full page; find how many full pages there are in the document (allowing for displays of various sorts, this number will probably not be an integer); multiply the two. However, if the document to be submitted is to determine the success of the rest of one's life, it takes a brave person to thumb their nose at authority quite so comprehensively...
The simplest method is to strip out the (La)TeX markup, and to count what's left. On a Unix-like system, this may be done using detex and the built-in wc:
detex <filename> | wc -wWinedt (see editors and shells) in the Windows environment provides this functionality direct.
Simply stripping (La)TeX markup isn't entirely reliable, however: that markup itself may contribute typeset words, and this could be a problem. The wordcount package contains a Bourne shell (i.e., typically Unix) script for running a LaTeX file with a special piece of supporting TeX code, and then counting word indications in the log file. This is probably as accurate automatic counting as you can get.